What is (\partial)/(\partial y)(y^5-3xy) ?

The answer to (\partial)/(\partial y)(y^5-3xy) is 5y^4-3x

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(\partial)/(\partial y)(y^5-3xy)

\frac{\partial}{\partial y} (y^{5} - 3 x y)

5 y^{4} - 3 x

Solution steps

\frac{\partial}{\partial y} (y^{5} - 3 x y)

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (y^{5}) - \frac{\partial}{\partial y} (3 x y)

\frac{\partial}{\partial y} (y^{5}) = 5 y^{4}

\frac{\partial}{\partial y} (3 x y) = 3 x

= 5 y^{4} - 3 x

\frac{d ^{2}}{d x ^{2}} (ln (x^{2} + 3 x + 15))

f (x) = 8 ln (x)

\int 3 x^{2} x^{3} - 2 d x

y^{^{'}} + 3 x y - 3 = 0

x \to 1 lim (3 x^{2} - 7 x + 1)

What is (\partial)/(\partial y)(y^5-3xy) ?
The answer to (\partial)/(\partial y)(y^5-3xy) is 5y^4-3x